The paper is organized as follows. In section 2, we briefly review the logarithmic correction to black hole entropy due to thermal fluctuations [1]}. In section 3, we obtain corrected thermodynamic quantities and investigate phase transition of the RN-AdS black hole in the presence of thermal fluctuations. We also compute critical exponents of the phase transition with small thermal fluctuations. Finally, we discuss our results in section 4. (We use the units \(G_{N} = \hbar = k_{B} = c = 1\) .)
